One glaring omission is that no one has mentioned how [$]e[$] came to be. Everyone blames Euler (some blame APL) but its roots are probably due to a 17th century banker or trader who stumbled on compound interest:

In Orson Scott Card’s Ender novels, one of the main characters grows very rich and lives for thousands of years by spending most of his time in interstellar travel at relativistic speeds. It seemed to me like it was so easy to earn fantastic sums through compound interest that more people would adopt that tactic and interest rates would plummet so that it no longer worked. The cost of course is that of travelling into the future and thus being left behind by social change, having your friends and family age and die, etc.

Put $1 in a bank account yielding exactly 2% continuously compounded and then check the account balance at noon in 252 years and 179 days.

Very good answer. I had not read this until this morning. But funnily the same idea crossed my mind yesterday.

So, the question was: How long does it take to earn $148.413 by investing $1 at a fixed rate of 2%?

Yep!

I also pondered if other exponential processes might be adapted to answer this question. But base-2 doubling requires an inconvenient 5/ln(2) = 7.213475 doublings to get the answer. And looking for the right seed for a Fibonacci process seemed to yield an answer of starting with 7457 and 12067 which after 10 cycles reaches 10000*e^5 with requisite accuracy but it feel like a hack!

It is conjectured that e is normal, i.e. when expressed in e.g. base 2 the digits are uniformly distributed, Homework.
On a related solution, how about computing e by Montmort's derangements (hat check problem).

This corresponds to a rapidity of w=5, that again correspond to a quite high relativistic doppler shift and a velocity ratio of
\(v/c=\tanh(5)\approx \) c x 0.999909204/c

someone would possibly call this a Pseudorapidity , but that is something different Pseudorapidity

in my max velocity theory: for rest-mass particles with this as max rapidity correspond to a hypothetical particle with reduced Compton wavelength of \(\bar{\lambda}=\frac{1}{2}e^5l_p\)

anyway I leave \(e^5\) to people doing sinful usury and mathematicians "that only are dealing with the structure of the reasoning...that don't even need to know what they are talking about...or what they they say is true.."

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Last edited by Collector on November 7th, 2017, 11:55 pm, edited 9 times in total.